Aw, thank you for rescuing this kitty!
It's probably not serious, but it's a good idea to figure what's causing the problem. It could be a sign of an upper respiratory infection (URI), it could simply be a result of herpes virus. Soooooo many kitties have herpes, it's quite common. URIs can be caused either by a virus or can be bacterial. Sometimes vets will give an antibiotic even if it's a viral infection just to help prevent secondary infections - but if it's caused by a virus, it would just need to run its course (just like with people).
Of course, some kitties have problems with their tear ducts.
For all of these reasons, it's a good idea to get her to the vet just to figure out what the source of the problem is, even if it's not serious.
If it is herpes, a supplement called L-lysine has been shown in clinical studies to reduce severity of flare-ups, shorten the length of flare-ups, and can prevent them altogether. Most of us on TCS use the NOW L-lysine powder. It has no taste and isn't toxic at ALL, so it's quite safe to use. The proper dose is 500mg (1/4 teaspoon) split into half in the morning and half at night given daily. For many of our kitties, this stops the herpes flare-ups altogether, and helps prevent URIs.
Just sprinkle it on or mix it into wet food, and she'll eat it right up.
